# Extended Formulas: Multiple Responses and Multiple Regressor Parts

### Description

The new class `Formula`

extends the base class
`formula`

by allowing for multiple responses
and multiple parts of regressors.

### Usage

1 2 3 4 5 6 7 8 |

### Arguments

`object, x` |
an object. For |

`lhs, rhs` |
indexes specifying which elements of the left- and
right-hand side, respectively, should be employed. |

`collapse` |
logical. Should multiple parts (if any) be collapsed
to a single part (essentially by replacing the |

`update` |
logical. Only used if |

`drop` |
logical. Should the |

`...` |
further arguments. |

### Details

`Formula`

objects extend the basic `formula`

objects.
These extensions include multi-part formulas such as
`y ~ x1 + x2 | u1 + u2 + u3 | v1 + v2`

, multiple response
formulas `y1 + y2 ~ x1 + x2 + x3`

, multi-part responses
such as `y1 | y2 + y3 ~ x`

, and combinations of these.

The `Formula`

creates a `Formula`

object from a `formula`

which can have the `|`

operator on the left- and/or right-hand
side (LHS and/or RHS). Essentially, it stores the original `formula`

along with attribute lists containing the decomposed parts for the LHS
and RHS, respectively.

The main motivation for providing the `Formula`

class is to be
able to conveniently compute model frames and model matrices or extract
selected responses based on an extended formula language. This functionality
is provided by methods to the generics `model.frame`

,
and `model.matrix`

. For details and examples, see
their manual page: `model.frame.Formula`

.

In addition to these workhorses, a few further methods and functions are provided.
By default, the `formula()`

method switches back to the original
`formula`

. Additionally, it allows selection of subsets of the
LHS and/or RHS (via `lhs`

, and `rhs`

) and collapsing
multiple parts on the LHS and/or RHS into a single part (via `collapse`

).

`is.Formula`

checks whether the argument inherits from the
`Formula`

class.

`as.Formula`

is a generic for coercing to `Formula`

, the
default method first coerces to `formula`

and then calls
`Formula`

. The default and `formula`

method also take an
optional `env`

argument, specifying the environment of the resulting
`Formula`

. In the latter case, this defaults to the environment
of the `formula`

supplied.

Methods to further standard generics `print`

,
`update`

, and `length`

are provided
for `Formula`

objects. The latter reports the number of parts on
the LHS and RHS, respectively.

### Value

`Formula`

returns an object of class `Formula`

which inherits from `formula`

. It is the original `formula`

plus two attributes `"lhs"`

and `"rhs"`

that contain the
parts of the decomposed left- and right-hand side, respectively.

### References

Zeileis A, Croissant Y (2010). Extended Model Formulas in R: Multiple Parts and Multiple Responses.
*Journal of Statistical Software*, **34**(1), 1–13.
http://www.jstatsoft.org/v34/i01/.

### See Also

`model.frame.Formula`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | ```
## create a simple Formula with one response and two regressor parts
f1 <- y ~ x1 + x2 | z1 + z2 + z3
F1 <- Formula(f1)
class(F1)
length(F1)
## switch back to original formula
formula(F1)
## create formula with various transformations
formula(F1, rhs = 1)
formula(F1, collapse = TRUE)
formula(F1, lhs = 0, rhs = 2)
## put it together from its parts
as.Formula(y ~ x1 + x2, ~ z1 + z2 + z3)
## update the formula
update(F1, . ~ . + I(x1^2) | . - z2 - z3)
update(F1, . | y2 + y3 ~ .)
# create a multi-response multi-part formula
f2 <- y1 | y2 + y3 ~ x1 + I(x2^2) | 0 + log(x1) | x3 / x4
F2 <- Formula(f2)
length(F2)
## obtain various subsets using standard indexing
## no lhs, first/seconde rhs
formula(F2, lhs = 0, rhs = 1:2)
formula(F2, lhs = 0, rhs = -3)
formula(F2, lhs = 0, rhs = c(TRUE, TRUE, FALSE))
## first lhs, third rhs
formula(F2, lhs = c(TRUE, FALSE), rhs = 3)
``` |

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